Question

Is the system of equations is consistent, consistent and coincident, or inconsistent?

Answer 1

Answer:

The given system of equations is inconsistent.

Step-by-step explanation:

We have been given a system of equations and we are asked to find whether our given system of equation is consistent, consistent and coincident, or inconsistent.

$y=-3x+12...(1)$        

$y=-6x+2...(2)$

Since we know that a system of equations is inconsistent if it has no solution. Parallel lines are inconsistent because they do not intersect.

Consistent system of equations can have one or infinitely many solution. As if two lines are same then they will have infinitely many solution. If lines intersect at only one point, then they will have only one solution.

Now let us check slope of given lines.

Upon dividing equation (2) by 2 we will get,

$y=-3x+1...(2)$

We can see that both lines have slope of negative 3. Since y-intercept of both equations are different, so they will not intersect at any point.

Since our given equations represent parallel lines, therefore, our given system of equations is inconsistent.

Answer 2

The slope of (y=-3x+12) is -3 while the slope of (y=-6x+2) is -6. Therefore, it's Inconsistent. 
Coincident is one line on the graph
Consistent is two parallel lines